In this analysis I used real data from Brazil Stock Market.

I will create a R package called r-stock-analysis https://github.com/caiomsouza/r-stock-analysis

http://www.thertrader.com

http://www.thertrader.com/2014/02/28/using-cart-for-stock-market-forecasting/

https://cran.r-project.org/web/packages/stocks/index.html

https://www.youtube.com/watch?v=iMET2gbsbHY

http://www.r-chart.com/2010/06/stock-analysis-using-r.html

TAREA 2: Cuantificación del riesgo de Mercado (primera del profesor Escot)

En esta tarea se trata de que apliquéis los métodos mostrados en clase para cuantificar el riesgo de mercado de los activos financieros.

1- Selección de variables: debeis seleccionar 5 valores (acciones) del mercado continuo español más el ibex 35 y bajar la serie completa. Para el punto 2 y 3 se utilizarán las series temporales completas hasta el 30 de septiembre de 2015. el mes de octubre se reservará para hacer predicciones

2.- ¿Son los mercados de estos 6 valores eficientes?

3.- ¿Se puede modelizar la serie de rendimientos diarios de estos valores?. ¿Que modelo predice mejor (utiliazando el error cuadrático medio)?

4.- Utilizando información de los dos últimos años. ¿cual es la mejor cartera que se puede formar con esos 5 valores?. Suponga para ello dos posibilidades, que los agentes son aversos al riesgos y no tienen otras alternativas de inversión (es deseable la cartera de menor riesgo); y en segundo lugar que existe la posibilidad de invertir (o endeudarse) a un tipo de interés sin riesgo del 0.5%. ¿Cómo se comportan estas carteras durante el mes de octubre mejor o peor que el ibex?. ¿Cual es la beta de los 5 valores? ¿y la beta de la cartera?, ¿cual de los cinco valores ha tenido un comportamiento mejor que lo esperado según la teoría del CAPM?

  1. Utilizando información del último año determine el valor en riesgo de su cartera óptima para el día uno de octubre de 2015 suponiendo que posee una riqueza financiera total de 1000 euros que tiene que repartir entre los cinco valores. Repita la estimación del Valor en riesgo para todos los días hábiles del mes de octubre y realice una prueba de estrés y una prueba de comprobación (backtesting) para saber si su estimación del VaR (Value at Risk) es correcta.

Por favor entregue un archivo word o pdf con los resultados principales de su trabajo explicando qué es lo que obtiene y que se deriva de dichos resultados. Puede incluir en el código R en el texto principal o al final del texto en un anexo, se valorará positivamente.

# UCM
# Prof. Lorenzo Escot
# Alumno: Caio Fernandes Moreno (caiofern@ucm.es)
# Brazil Stock Market Analysis




setwd("~/git/Bitbucket/ucm/SCORE/tareas/Lorenzo-Escot")

library(tseries) # adf.test, kpss.test, bds.test, get.hist.quote, portfolio.optim, surrogate, arma, garch
#install.packages("forecast")
library(forecast)
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## 
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## Loading required package: timeDate
## This is forecast 6.2
# En el paquete forecast tiene un modelo auto ARIMA.
#install.packages("fArma")
library(fArma) #ARMAFIT, RSFIT
## Loading required package: timeSeries
## 
## Attaching package: 'timeSeries'
## 
## The following object is masked from 'package:zoo':
## 
##     time<-
## 
## Loading required package: fBasics
## 
## 
## Rmetrics Package fBasics
## Analysing Markets and calculating Basic Statistics
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.org
#install.packages("fGarch")
library(fGarch) #GARCHFIT formula ~arma (2,1) + garch (1,1) # ~ AltGr + 4
#install.packages("outliers")
library(outliers) #: outlier, rm.outlier, scores, chisq.out.test # para detectar outliers o datos an?malos ojo serie estacionaria
## 
## Attaching package: 'outliers'
## 
## The following object is masked from 'package:timeSeries':
## 
##     outlier
#install.packages("zoo")
library(zoo)
#setinternet2() #esto abre el puerto de internet



#stock.name <- "^BVSP"
#stock.description <- "IBOVESPA"



generateAnalysis <- function(x, y) {
  

stock.name <- x 
stock.description <- y  
  
  
## lectura de los datos hist?ricos del ^BVSP
stock.name <- get.hist.quote(instrument=stock.name, quote="AdjClose")

# BVSP time series starts 1993-04-27
# http://finance.yahoo.com/q?s=%5EBVSP

series.name <- stock.name

str(series.name)
summary(series.name)
start(series.name)
end(series.name)
plot(series.name)

head(series.name, 10)

tail(series.name, 10)

# Mirando los datos he decidido con la ayuda del Prof. Lorenzo no quitar los datos de 1993 hasta 1998.

#?existen datos nulos?
length(series.name)
length(series.name[!is.na(series.name)])
length(complete.cases(series.name))
#parece que no, pero si tuviera na se podr?an quitar con: ibex<-ibex[complete.cases(ibex)]

series.name<-series.name[complete.cases(series.name)]
plot(series.name)


### podemos seleccionar una submuestra: Temporal
series.name.short <-window(series.name,start=as.Date("1993-04-27"),end=as.Date("2015-09-30"))
str(series.name.short)
summary(series.name.short)
plot(series.name.short)


## Calculo la serie de rendimientos
d.series.name <- diff(log(series.name.short))

# Concatenate stock.description with the text Withall
plot.description <- paste(stock.description, "WITH ALL DATA", collapse = ", ")

#Grafico de la serie 
plot(d.series.name, main=(plot.description))

     

     
#Datos an?malos
# type = z Busca los datos tipificados mayor que 5 vezes la sd (disviacion tipica)

# Remove datos anomalos
remove.outlier.d.series.name <- d.series.name[abs(scores(d.series.name, type="z"))<=5]

#plot(remove.outlier.d.series.name, main="IBOVESPA WITHOUT OUTLIERS")

# Concatenate stock.description with the text Withall
plot.description <- paste(stock.description, " WITHOUT OUTLIERS", collapse = ", ")

#Grafico de la serie 
plot(d.series.name, main=(plot.description))


#?es estacionario?
adf.test(d.series.name)# Ho: una ra?z unitaria (no estacionaria)

# Augmented Dickey-Fuller Test
# data:  dBVSP
# Dickey-Fuller = -14.073, Lag order = 17, p-value = 0.01
# alternative hypothesis: stationary

# No es estacionaria

sd(d.series.name) #desviaci?n t?pica

# Statistical stationarity:
# http://people.duke.edu/~rnau/411diff.htm


#?presenta correlaci?n?

df.d.series.name <- as.data.frame(d.series.name)

#periodograma
par(mfrow=c(2,1))
acf(df.d.series.name, ylim=c(-1,1)) 
pacf(df.d.series.name, ylim=c(-1,1))


tsdisplay(df.d.series.name)


# test bds
bds.test(d.series.name,m=10) # H0: i.i.d

#test R/, exponente de Hurst
HURST<-rsFit(d.series.name, doplot = T)# Exponente de Hurst 0.5 ruido blanco
HURST

##Se puede hacer el test de Hurst=0.5 con el siguiente estad?stico t ## 

t<-(HURST@hurst$diag[2,1]-0.5)/HURST@hurst$diag[2,2]
t

#Modelo Auto Arima

modelo.auto.arima <- auto.arima(d.series.name)
plot(forecast(modelo.auto.arima,h=20))


modelo.auto.arima1 <- auto.arima(d.series.name)
plot(forecast(modelo.auto.arima1, h=1))


# alternativa
d.series.name.ARMA<-armaFit(~ arma(1,3), data=d.series.name)
summary(d.series.name.ARMA, wich="all")
residuo<-residuals(d.series.name.ARMA)


plot(residuo)
lines(residuo)

df.residuo <- as.data.frame(residuo)

#periodograma
par(mfrow=c(2,1))
acf(df.residuo, ylim=c(-1,1)) 
pacf(df.residuo, ylim=c(-1,1))

#x11()
tsdisplay(df.residuo)


# test bds
bds.test(d.series.name,m=10) # H0: i.i.d

#test R/, exponente de Hurst
HURST<-rsFit(d.series.name, doplot = T)# Exponente de Hurst 0.5 ruido blanco
HURST


# Este codigo ha tenido muchas modificaciones hay que cojer el codigo del profesor Lorenzo.

##Se puede hacer el test de Hurst=0.5 con el siguiente estad?stico t ## 

t<-(HURST@hurst$diag[2,1]-0.5)/HURST@hurst$diag[2,2]
t


####PREDICCIONES
predict(d.series.name.ARMA, n.ahead=10, conf=c(90,95), dplot=True)


#alternativo
d.series.name.ARMAGARCH<-garchFit(~ arma(1,1) + garch(2,1), data=d.series.name, include.mean=TRUE) ####aqu? el orden es GARCH,ARCH
summary(d.series.name.ARMAGARCH)
plot(d.series.name.ARMAGARCH@residuals)
residuogarch<-residuals(d.series.name.ARMAGARCH)
volatilitygarch<-volatility(d.series.name.ARMAGARCH)
plot(volatilitygarch)
lines(volatilitygarch)
plot(d.series.name^2)

predict(d.series.name.ARMAGARCH, n.ahead=10, conf=c(90,95), dplot=TRUE)


}



# IBOVESPA
stock.name <- "^BVSP"
stock.description <- "IBOVESPA"
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)
## time series starts 1993-04-27
## 'zoo' series from 1993-04-27 to 2016-01-06
##   Data: num [1:5635, 1] 24.5 24.3 23.7 24.1 24.1 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "AdjClose"
##   Index:  Date[1:5635], format: "1993-04-27" "1993-04-28" "1993-04-29" "1993-04-30" ...

## 'zoo' series from 1993-04-27 to 2015-09-30
##   Data: num [1:5572] 24.5 24.3 23.7 24.1 24.1 ...
##   Index:  Date[1:5572], format: "1993-04-27" "1993-04-28" "1993-04-29" "1993-04-30" ...

## Warning in adf.test(d.series.name): p-value smaller than printed p-value

## Warning in sqrt(diag(fit$var.coef)): NaNs produced

## 
## Title:
##  ARIMA Modelling 
## 
## Call:
##  armaFit(formula = ~arma(1, 3), data = d.series.name)
## 
## Model:
##  ARIMA(1,0,3) with method: CSS-ML
## 
## Coefficient(s):
##       ar1        ma1        ma2        ma3  intercept  
##  0.028451   0.027562  -0.006066  -0.012289   0.001349  
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1724656 -0.0116332 -0.0002197  0.0116098  0.2916280 
## 
## Moments: 
## Skewness Kurtosis 
##   0.5518  10.4767 
## 
## Coefficient(s):
##             Estimate  Std. Error  t value Pr(>|t|)    
## ar1        0.0284509          NA       NA       NA    
## ma1        0.0275620          NA       NA       NA    
## ma2       -0.0060665          NA       NA       NA    
## ma3       -0.0122894   0.0034857   -3.526 0.000422 ***
## intercept  0.0013495   0.0003251    4.151 3.31e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## sigma^2 estimated as: 0.0005446
## log likelihood:       13029.24
## AIC Criterion:        -26046.48

## 
## Description:
##  Thu Jan  7 16:12:14 2016 by user:

## 
## Series Initialization:
##  ARMA Model:                arma
##  Formula Mean:              ~ arma(1, 1)
##  GARCH Model:               garch
##  Formula Variance:          ~ garch(2, 1)
##  ARMA Order:                1 1
##  Max ARMA Order:            1
##  GARCH Order:               2 1
##  Max GARCH Order:           2
##  Maximum Order:             2
##  Conditional Dist:          norm
##  h.start:                   3
##  llh.start:                 1
##  Length of Series:          5571
##  Recursion Init:            mci
##  Series Scale:              0.02337828
## 
## Parameter Initialization:
##  Initial Parameters:          $params
##  Limits of Transformations:   $U, $V
##  Which Parameters are Fixed?  $includes
##  Parameter Matrix:
##                      U           V      params includes
##     mu     -0.57716768   0.5771677  0.05772286     TRUE
##     ar1    -0.99999999   1.0000000 -0.04584008     TRUE
##     ma1    -0.99999999   1.0000000  0.10215077     TRUE
##     omega   0.00000100 100.0000000  0.10000000     TRUE
##     alpha1  0.00000001   1.0000000  0.05000000     TRUE
##     alpha2  0.00000001   1.0000000  0.05000000     TRUE
##     gamma1 -0.99999999   1.0000000  0.10000000    FALSE
##     gamma2 -0.99999999   1.0000000  0.10000000    FALSE
##     beta1   0.00000001   1.0000000  0.80000000     TRUE
##     delta   0.00000000   2.0000000  2.00000000    FALSE
##     skew    0.10000000  10.0000000  1.00000000    FALSE
##     shape   1.00000000  10.0000000  4.00000000    FALSE
##  Index List of Parameters to be Optimized:
##     mu    ar1    ma1  omega alpha1 alpha2  beta1 
##      1      2      3      4      5      6      9 
##  Persistence:                  0.9 
## 
## 
## --- START OF TRACE ---
## Selected Algorithm: nlminb 
## 
## R coded nlminb Solver: 
## 
##   0:     7007.5070: 0.0577229 -0.0458401 0.102151 0.100000 0.0500000 0.0500000 0.800000
##   1:     6912.5211: 0.0577222 -0.0462831 0.101731 0.0745310 0.0495072 0.0487042 0.786314
##   2:     6853.3005: 0.0577207 -0.0470350 0.101025 0.0634282 0.0685389 0.0667259 0.791504
##   3:     6836.3228: 0.0577203 -0.0472069 0.100865 0.0568509 0.0683983 0.0664953 0.789530
##   4:     6820.2471: 0.0577188 -0.0477502 0.100360 0.0438816 0.0716566 0.0695678 0.788959
##   5:     6812.6945: 0.0577096 -0.0502291 0.0980834 0.0378664 0.0817180 0.0812599 0.810664
##   6:     6805.5983: 0.0576893 -0.0540431 0.0946779 0.0164254 0.0748376 0.0771232 0.825021
##   7:     6794.9712: 0.0575556 -0.0718150 0.0795594 0.0237874 0.0753770 0.0716922 0.836102
##   8:     6788.5061: 0.0574791 -0.0557498 0.0969688 0.0199860 0.0745192 0.0629286 0.846183
##   9:     6787.9674: 0.0574787 -0.0557881 0.0969381 0.0190952 0.0740933 0.0624548 0.845810
##  10:     6787.5205: 0.0574688 -0.0566813 0.0962259 0.0199000 0.0719904 0.0593221 0.848100
##  11:     6787.4584: 0.0574596 -0.0573165 0.0957600 0.0170137 0.0729269 0.0590613 0.851498
##  12:     6786.9905: 0.0574435 -0.0578171 0.0955500 0.0178711 0.0729353 0.0566919 0.855337
##  13:     6786.3007: 0.0574238 -0.0583268 0.0953934 0.0166574 0.0727417 0.0533564 0.858240
##  14:     6785.0358: 0.0573042 -0.0609257 0.0949264 0.0147055 0.0756105 0.0374833 0.873206
##  15:     6784.9513: 0.0573039 -0.0609300 0.0949275 0.0144428 0.0754729 0.0373121 0.873049
##  16:     6784.9178: 0.0573005 -0.0609769 0.0949412 0.0148881 0.0752191 0.0367046 0.872989
##  17:     6784.8955: 0.0572891 -0.0610873 0.0950334 0.0148109 0.0757447 0.0361657 0.872897
##  18:     6784.8194: 0.0572043 -0.0618735 0.0957554 0.0150197 0.0791459 0.0331976 0.872542
##  19:     6784.8080: 0.0569791 -0.0636508 0.0980053 0.0146289 0.0789961 0.0327952 0.872790
##  20:     6784.7182: 0.0567522 -0.0654953 0.100181 0.0148012 0.0789341 0.0327467 0.873255
##  21:     6784.2295: 0.0518477 -0.109835 0.139305 0.0136174 0.0757387 0.0313714 0.878754
##  22:     6784.1406: 0.0511277 -0.113360 0.147435 0.0135018 0.0758185 0.0301757 0.880208
##  23:     6784.0039: 0.0503543 -0.116973 0.149390 0.0138244 0.0803689 0.0257012 0.879560
##  24:     6784.0031: 0.0503540 -0.116965 0.149401 0.0137353 0.0804061 0.0256993 0.879575
##  25:     6784.0014: 0.0503509 -0.116926 0.149379 0.0137706 0.0804440 0.0256933 0.879620
##  26:     6784.0006: 0.0503467 -0.116889 0.149364 0.0137362 0.0804623 0.0256583 0.879637
##  27:     6783.9995: 0.0503375 -0.116818 0.149332 0.0137450 0.0805052 0.0256090 0.879689
##  28:     6783.9886: 0.0501455 -0.115640 0.148781 0.0136994 0.0808562 0.0245808 0.880245
##  29:     6783.9846: 0.0500002 -0.113680 0.146786 0.0136566 0.0810501 0.0244768 0.880418
##  30:     6783.9807: 0.0498245 -0.112089 0.145224 0.0135753 0.0811067 0.0244143 0.880404
##  31:     6783.9734: 0.0488638 -0.107401 0.141045 0.0136648 0.0811885 0.0248538 0.879887
##  32:     6783.9621: 0.0482468 -0.0977786 0.130713 0.0134019 0.0819212 0.0235134 0.880859
##  33:     6783.9523: 0.0474507 -0.105218 0.138210 0.0134022 0.0835961 0.0203012 0.882299
##  34:     6783.9500: 0.0474507 -0.105220 0.138209 0.0132982 0.0835712 0.0202772 0.882257
##  35:     6783.9484: 0.0474539 -0.105285 0.138273 0.0133313 0.0835901 0.0203023 0.882275
##  36:     6783.9481: 0.0474599 -0.105422 0.138394 0.0132626 0.0836327 0.0203670 0.882278
##  37:     6783.9477: 0.0474707 -0.105728 0.138694 0.0132844 0.0836298 0.0204006 0.882266
##  38:     6783.9464: 0.0475954 -0.110869 0.143667 0.0133533 0.0833928 0.0209793 0.881851
##  39:     6783.9463: 0.0474949 -0.108712 0.141564 0.0133731 0.0831606 0.0213533 0.881696
##  40:     6783.9463: 0.0477035 -0.113348 0.146237 0.0133731 0.0832319 0.0212893 0.881691
##  41:     6783.9463: 0.0475918 -0.111389 0.144202 0.0133688 0.0832613 0.0212018 0.881746
##  42:     6783.9463: 0.0475979 -0.111229 0.144069 0.0133695 0.0832390 0.0212428 0.881729
##  43:     6783.9463: 0.0476014 -0.111364 0.144201 0.0133697 0.0832420 0.0212388 0.881730
## 
## Final Estimate of the Negative LLH:
##  LLH:  -14140.44    norm LLH:  -2.538223 
##            mu           ar1           ma1         omega        alpha1 
##  1.112838e-03 -1.113636e-01  1.442007e-01  7.307105e-06  8.324200e-02 
##        alpha2         beta1 
##  2.123883e-02  8.817298e-01 
## 
## R-optimhess Difference Approximated Hessian Matrix:
##                   mu         ar1         ma1         omega        alpha1
## mu     -1.549541e+07 -10973.6813   4394.0775  1.001200e+08  8.825238e+03
## ar1    -1.097368e+04  -5220.4525  -5213.6790  2.855247e+05  1.579227e+02
## ma1     4.394078e+03  -5213.6790  -5232.8327  2.416058e+05  1.471186e+02
## omega   1.001200e+08 285524.6926 241605.8057 -3.215057e+12 -5.470996e+08
## alpha1  8.825238e+03    157.9227    147.1186 -5.470996e+08 -1.621422e+05
## alpha2  9.952543e+02    199.6427    198.0982 -5.611563e+08 -1.616199e+05
## beta1  -1.252181e+04   -309.0611   -291.8503 -7.660070e+08 -1.853151e+05
##               alpha2         beta1
## mu      9.952543e+02 -1.252181e+04
## ar1     1.996427e+02 -3.090611e+02
## ma1     1.980982e+02 -2.918503e+02
## omega  -5.611563e+08 -7.660070e+08
## alpha1 -1.616199e+05 -1.853151e+05
## alpha2 -1.659141e+05 -1.908219e+05
## beta1  -1.908219e+05 -2.369930e+05
## attr(,"time")
## Time difference of 0.213238 secs
## 
## --- END OF TRACE ---
## 
## 
## Time to Estimate Parameters:
##  Time difference of 0.802696 secs
## 
## Title:
##  GARCH Modelling 
## 
## Call:
##  garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name, 
##     include.mean = TRUE) 
## 
## Mean and Variance Equation:
##  data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1bdddbaa0>
##  [data = d.series.name]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##          mu          ar1          ma1        omega       alpha1  
##  1.1128e-03  -1.1136e-01   1.4420e-01   7.3071e-06   8.3242e-02  
##      alpha2        beta1  
##  2.1239e-02   8.8173e-01  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##          Estimate  Std. Error  t value Pr(>|t|)    
## mu      1.113e-03   3.965e-04    2.807    0.005 ** 
## ar1    -1.114e-01   3.066e-01   -0.363    0.716    
## ma1     1.442e-01   3.060e-01    0.471    0.637    
## omega   7.307e-06   1.445e-06    5.056 4.29e-07 ***
## alpha1  8.324e-02   1.467e-02    5.673 1.41e-08 ***
## alpha2  2.124e-02   1.906e-02    1.114    0.265    
## beta1   8.817e-01   1.257e-02   70.121  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log Likelihood:
##  14140.44    normalized:  2.538223 
## 
## Description:
##  Thu Jan  7 16:12:16 2016 by user:  
## 
## 
## Standardised Residuals Tests:
##                                 Statistic p-Value     
##  Jarque-Bera Test   R    Chi^2  383.587   0           
##  Shapiro-Wilk Test  R    W      NA        NA          
##  Ljung-Box Test     R    Q(10)  22.13172  0.01444747  
##  Ljung-Box Test     R    Q(15)  34.83257  0.002597619 
##  Ljung-Box Test     R    Q(20)  49.09035  0.0002985119
##  Ljung-Box Test     R^2  Q(10)  21.52159  0.0177362   
##  Ljung-Box Test     R^2  Q(15)  24.39986  0.05860695  
##  Ljung-Box Test     R^2  Q(20)  36.64023  0.01291958  
##  LM Arch Test       R    TR^2   23.01995  0.02755703  
## 
## Information Criterion Statistics:
##       AIC       BIC       SIC      HQIC 
## -5.073933 -5.065608 -5.073936 -5.071031

# Itau
stock.name <- "ITSA4.SA"
stock.description <- "Itausa - Investimentos Itau S.A"
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)
## time series starts 2000-01-03
## 'zoo' series from 2000-01-03 to 2016-01-06
##   Data: num [1:3989, 1] 1.14 1.03 1.12 1.13 1.13 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "AdjClose"
##   Index:  Date[1:3989], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...

## 'zoo' series from 2000-01-03 to 2015-09-30
##   Data: num [1:3919] 1.14 1.03 1.12 1.13 1.13 ...
##   Index:  Date[1:3919], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...

## Warning in adf.test(d.series.name): p-value smaller than printed p-value

## Warning in sqrt(diag(fit$var.coef)): NaNs produced

## 
## Title:
##  ARIMA Modelling 
## 
## Call:
##  armaFit(formula = ~arma(1, 3), data = d.series.name)
## 
## Model:
##  ARIMA(1,0,3) with method: CSS-ML
## 
## Coefficient(s):
##        ar1         ma1         ma2         ma3   intercept  
## -0.4622035   0.4578396  -0.0348802  -0.0624000   0.0004784  
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1513910 -0.0126070 -0.0004014  0.0120342  0.2207431 
## 
## Moments: 
## Skewness Kurtosis 
##   0.1585   5.8397 
## 
## Coefficient(s):
##             Estimate  Std. Error  t value Pr(>|t|)    
## ar1       -0.4622035          NA       NA       NA    
## ma1        0.4578396          NA       NA       NA    
## ma2       -0.0348802   0.0180969   -1.927 0.053928 .  
## ma3       -0.0624000   0.0160788   -3.881 0.000104 ***
## intercept  0.0004784   0.0003490    1.371 0.170464    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## sigma^2 estimated as: 0.00055
## log likelihood:       9144.02
## AIC Criterion:        -18276.04

## 
## Description:
##  Thu Jan  7 16:12:23 2016 by user:

## 
## Series Initialization:
##  ARMA Model:                arma
##  Formula Mean:              ~ arma(1, 1)
##  GARCH Model:               garch
##  Formula Variance:          ~ garch(2, 1)
##  ARMA Order:                1 1
##  Max ARMA Order:            1
##  GARCH Order:               2 1
##  Max GARCH Order:           2
##  Maximum Order:             2
##  Conditional Dist:          norm
##  h.start:                   3
##  llh.start:                 1
##  Length of Series:          3918
##  Recursion Init:            mci
##  Series Scale:              0.02349959
## Warning in arima(.series$x, order = c(u, 0, v), include.mean =
## include.mean): possible convergence problem: optim gave code = 1

## Parameter Initialization:
##  Initial Parameters:          $params
##  Limits of Transformations:   $U, $V
##  Which Parameters are Fixed?  $includes
##  Parameter Matrix:
##                      U           V      params includes
##     mu     -0.19735249   0.1973525  0.02116543     TRUE
##     ar1    -0.99999999   1.0000000 -0.55064704     TRUE
##     ma1    -0.99999999   1.0000000  0.54580383     TRUE
##     omega   0.00000100 100.0000000  0.10000000     TRUE
##     alpha1  0.00000001   1.0000000  0.05000000     TRUE
##     alpha2  0.00000001   1.0000000  0.05000000     TRUE
##     gamma1 -0.99999999   1.0000000  0.10000000    FALSE
##     gamma2 -0.99999999   1.0000000  0.10000000    FALSE
##     beta1   0.00000001   1.0000000  0.80000000     TRUE
##     delta   0.00000000   2.0000000  2.00000000    FALSE
##     skew    0.10000000  10.0000000  1.00000000    FALSE
##     shape   1.00000000  10.0000000  4.00000000    FALSE
##  Index List of Parameters to be Optimized:
##     mu    ar1    ma1  omega alpha1 alpha2  beta1 
##      1      2      3      4      5      6      9 
##  Persistence:                  0.9 
## 
## 
## --- START OF TRACE ---
## Selected Algorithm: nlminb 
## 
## R coded nlminb Solver: 
## 
##   0:     5242.2289: 0.0211654 -0.550647 0.545804 0.100000 0.0500000 0.0500000 0.800000
##   1:     5237.9398: 0.0211656 -0.550584 0.545775 0.0939968 0.0490868 0.0485212 0.796818
##   2:     5234.0814: 0.0211666 -0.550259 0.545674 0.0863456 0.0586183 0.0554934 0.799969
##   3:     5232.4526: 0.0211668 -0.550164 0.545682 0.0827873 0.0576379 0.0541377 0.798412
##   4:     5231.1120: 0.0211684 -0.549485 0.545760 0.0768023 0.0632714 0.0571542 0.803834
##   5:     5228.4869: 0.0211732 -0.547391 0.546017 0.0634602 0.0616730 0.0493813 0.817273
##   6:     5224.4317: 0.0211792 -0.546533 0.544587 0.0575780 0.0627765 0.0425538 0.835734
##   7:     5215.2208: 0.0212023 -0.551108 0.531163 0.0259704 0.0622625 0.00725046 0.901836
##   8:     5214.9234: 0.0212023 -0.551028 0.531228 0.0265262 0.0625851 0.00748926 0.902286
##   9:     5214.8008: 0.0212028 -0.550154 0.531939 0.0265851 0.0622761 0.00620402 0.902614
##  10:     5214.5388: 0.0212107 -0.546809 0.532779 0.0270990 0.0624737 0.00640765 0.902971
##  11:     5214.4154: 0.0212189 -0.543425 0.533580 0.0268713 0.0621906 0.00616550 0.902723
##  12:     5214.4069: 0.0212276 -0.540025 0.534245 0.0273328 0.0623636 0.00639938 0.902906
##  13:     5214.3535: 0.0212336 -0.538571 0.533713 0.0272686 0.0625448 0.00584667 0.902361
##  14:     5214.3057: 0.0212329 -0.539762 0.532631 0.0274683 0.0631157 0.00542864 0.902354
##  15:     5214.2823: 0.0212456 -0.537773 0.530303 0.0272307 0.0640549 0.00411904 0.902070
##  16:     5214.1604: 0.0212585 -0.534537 0.529278 0.0276119 0.0646694 0.00389914 0.902135
##  17:     5214.1006: 0.0212858 -0.528582 0.526218 0.0264993 0.0649148 0.00298597 0.903237
##  18:     5214.0354: 0.0213236 -0.528870 0.513870 0.0244897 0.0613136 0.00410330 0.908325
##  19:     5214.0085: 0.0213237 -0.528819 0.513907 0.0246519 0.0614323 0.00412083 0.908466
##  20:     5213.9899: 0.0213238 -0.528713 0.513986 0.0246078 0.0614356 0.00390835 0.908465
##  21:     5213.9696: 0.0213255 -0.528374 0.513781 0.0247883 0.0616028 0.00377062 0.908581
##  22:     5213.9422: 0.0213298 -0.527716 0.513123 0.0247787 0.0616677 0.00346540 0.908431
##  23:     5213.9081: 0.0213387 -0.526378 0.511765 0.0250607 0.0620297 0.00317671 0.908370
##  24:     5213.8574: 0.0213573 -0.523642 0.508996 0.0251212 0.0624005 0.00278153 0.907931
##  25:     5213.6207: 0.0215468 -0.495338 0.484540 0.0244704 0.0635385 0.00417500 0.906968
##  26:     5213.4552: 0.0217446 -0.468101 0.459081 0.0254614 0.0623108 0.00246697 0.906866
##  27:     5213.4479: 0.0219552 -0.442049 0.432787 0.0276590 0.0645128 0.00152952 0.905667
##  28:     5213.1813: 0.0220374 -0.437776 0.427382 0.0277873 0.0661175 0.000118229 0.903692
##  29:     5213.1167: 0.0221486 -0.434467 0.426867 0.0264039 0.0625110 0.00208115 0.907099
##  30:     5213.0916: 0.0221487 -0.434445 0.426880 0.0260543 0.0626483 0.00197831 0.907099
##  31:     5213.0692: 0.0221534 -0.434381 0.426818 0.0261019 0.0628864 0.00203949 0.907252
##  32:     5213.0483: 0.0221653 -0.434100 0.426532 0.0258801 0.0630060 0.00189263 0.907192
##  33:     5213.0248: 0.0221881 -0.433403 0.425819 0.0259048 0.0633145 0.00185943 0.907282
##  34:     5212.9961: 0.0222300 -0.431813 0.424211 0.0257431 0.0635391 0.00162834 0.907165
##  35:     5212.9575: 0.0223075 -0.428398 0.420799 0.0258311 0.0639807 0.00144657 0.907152
##  36:     5212.8054: 0.0232118 -0.394487 0.387162 0.0261158 0.0654414 1.00000e-08 0.906061
##  37:     5212.5833: 0.0257159 -0.422872 0.412330 0.0248318 0.0674655 1.00000e-08 0.906331
##  38:     5212.5678: 0.0257159 -0.422846 0.412353 0.0249798 0.0675083 1.00000e-08 0.906457
##  39:     5212.5558: 0.0257163 -0.422627 0.412545 0.0249481 0.0670954 1.00000e-08 0.906549
##  40:     5212.5439: 0.0257363 -0.422570 0.412535 0.0250631 0.0671285 1.00000e-08 0.906673
##  41:     5212.5356: 0.0257766 -0.422421 0.412537 0.0249879 0.0669704 1.00000e-08 0.906720
##  42:     5212.5232: 0.0258577 -0.422252 0.412417 0.0250455 0.0669515 1.00000e-08 0.906842
##  43:     5211.5509: 0.0445587 -0.388189 0.377516 0.0224797 0.0597943 1.00000e-08 0.915669
##  44:     5211.2496: 0.0516639 -0.377569 0.375124 0.0244132 0.0634322 1.00000e-08 0.910325
##  45:     5211.1828: 0.0574399 -0.447700 0.442259 0.0234704 0.0650098 1.00000e-08 0.910459
##  46:     5211.1390: 0.0582842 -0.423568 0.415022 0.0235889 0.0658549 1.00000e-08 0.909636
##  47:     5211.1121: 0.0572153 -0.412415 0.405121 0.0238046 0.0654789 1.00000e-08 0.909554
##  48:     5211.1087: 0.0565741 -0.406631 0.399915 0.0238993 0.0652300 1.00000e-08 0.909608
##  49:     5211.1087: 0.0565897 -0.406560 0.399838 0.0239019 0.0652405 1.00000e-08 0.909592
##  50:     5211.1087: 0.0565884 -0.406549 0.399826 0.0239017 0.0652404 1.00000e-08 0.909593
## 
## Final Estimate of the Negative LLH:
##  LLH:  -9484.418    norm LLH:  -2.420729 
##            mu           ar1           ma1         omega        alpha1 
##  1.329805e-03 -4.065493e-01  3.998263e-01  1.319924e-05  6.524036e-02 
##        alpha2         beta1 
##  1.000000e-08  9.095929e-01 
## 
## R-optimhess Difference Approximated Hessian Matrix:
##                   mu           ar1           ma1         omega
## mu      -5024279.809   -3118.73091    1471.74511 -6.502179e+07
## ar1        -3118.731   -4103.35508   -4052.80869 -3.332937e+05
## ma1         1471.745   -4052.80869   -4075.27825 -2.683192e+05
## omega  -65021785.290 -333293.72547 -268319.17123 -1.540547e+12
## alpha1     -2086.051     237.30353     248.60591 -4.750227e+08
## alpha2     -4629.759      23.75007      30.52669 -4.797590e+08
## beta1     -24801.877    -465.62881    -438.75675 -6.097617e+08
##               alpha1        alpha2         beta1
## mu     -2.086051e+03 -4.629759e+03 -2.480188e+04
## ar1     2.373035e+02  2.375007e+01 -4.656288e+02
## ma1     2.486059e+02  3.052669e+01 -4.387568e+02
## omega  -4.750227e+08 -4.797590e+08 -6.097617e+08
## alpha1 -2.035722e+05 -2.024629e+05 -2.224960e+05
## alpha2 -2.024629e+05 -2.062615e+05 -2.265880e+05
## beta1  -2.224960e+05 -2.265880e+05 -2.702168e+05
## attr(,"time")
## Time difference of 0.1453691 secs
## 
## --- END OF TRACE ---
## 
## 
## Time to Estimate Parameters:
##  Time difference of 0.6953762 secs
## 
## Title:
##  GARCH Modelling 
## 
## Call:
##  garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name, 
##     include.mean = TRUE) 
## 
## Mean and Variance Equation:
##  data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b9071f08>
##  [data = d.series.name]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##          mu          ar1          ma1        omega       alpha1  
##  1.3298e-03  -4.0655e-01   3.9983e-01   1.3199e-05   6.5240e-02  
##      alpha2        beta1  
##  1.0000e-08   9.0959e-01  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##          Estimate  Std. Error  t value Pr(>|t|)    
## mu      1.330e-03   4.606e-04    2.887 0.003885 ** 
## ar1    -4.065e-01   1.206e-01   -3.370 0.000752 ***
## ma1     3.998e-01   1.210e-01    3.303 0.000956 ***
## omega   1.320e-05   3.164e-06    4.171 3.03e-05 ***
## alpha1  6.524e-02   1.460e-02    4.468 7.88e-06 ***
## alpha2  1.000e-08   1.823e-02    0.000 1.000000    
## beta1   9.096e-01   1.411e-02   64.487  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log Likelihood:
##  9484.418    normalized:  2.420729 
## 
## Description:
##  Thu Jan  7 16:12:25 2016 by user:  
## 
## 
## Standardised Residuals Tests:
##                                 Statistic p-Value   
##  Jarque-Bera Test   R    Chi^2  972.8185  0         
##  Shapiro-Wilk Test  R    W      0.9809267 0         
##  Ljung-Box Test     R    Q(10)  18.93227  0.04113149
##  Ljung-Box Test     R    Q(15)  22.2451   0.1015363 
##  Ljung-Box Test     R    Q(20)  26.26359  0.1572818 
##  Ljung-Box Test     R^2  Q(10)  8.41126   0.5887326 
##  Ljung-Box Test     R^2  Q(15)  11.84018  0.6910838 
##  Ljung-Box Test     R^2  Q(20)  13.71289  0.8447494 
##  LM Arch Test       R    TR^2   10.65483  0.5587085 
## 
## Information Criterion Statistics:
##       AIC       BIC       SIC      HQIC 
## -4.837886 -4.826677 -4.837892 -4.833908

# BBAS3.SA
stock.name <- "BBAS3.SA"
stock.description <- "Banco do Brasil S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)
## time series starts 2000-01-03
## 'zoo' series from 2000-01-03 to 2016-01-06
##   Data: num [1:4134, 1] 1.86 1.78 1.79 1.82 1.78 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "AdjClose"
##   Index:  Date[1:4134], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...

## 'zoo' series from 2000-01-03 to 2015-09-30
##   Data: num [1:4064] 1.86 1.78 1.79 1.82 1.78 ...
##   Index:  Date[1:4064], format: "2000-01-03" "2000-01-04" "2000-01-05" "2000-01-06" ...

## Warning in adf.test(d.series.name): p-value smaller than printed p-value

## Warning in sqrt(diag(fit$var.coef)): NaNs produced

## 
## Title:
##  ARIMA Modelling 
## 
## Call:
##  armaFit(formula = ~arma(1, 3), data = d.series.name)
## 
## Model:
##  ARIMA(1,0,3) with method: CSS-ML
## 
## Coefficient(s):
##        ar1         ma1         ma2         ma3   intercept  
## -0.0060656  -0.0058871  -0.0409494  -0.0208757   0.0005117  
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.164227 -0.015215 -0.000486  0.014395  0.256153 
## 
## Moments: 
## Skewness Kurtosis 
##    0.405    5.096 
## 
## Coefficient(s):
##             Estimate  Std. Error  t value Pr(>|t|)    
## ar1       -0.0060656          NA       NA       NA    
## ma1       -0.0058871          NA       NA       NA    
## ma2       -0.0409494   0.0112843   -3.629 0.000285 ***
## ma3       -0.0208757          NA       NA       NA    
## intercept  0.0005117   0.0003929    1.302 0.192872    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## sigma^2 estimated as: 0.0007293
## log likelihood:       8909.2
## AIC Criterion:        -17806.4

## 
## Description:
##  Thu Jan  7 16:12:32 2016 by user:

## 
## Series Initialization:
##  ARMA Model:                arma
##  Formula Mean:              ~ arma(1, 1)
##  GARCH Model:               garch
##  Formula Variance:          ~ garch(2, 1)
##  ARMA Order:                1 1
##  Max ARMA Order:            1
##  GARCH Order:               2 1
##  Max GARCH Order:           2
##  Maximum Order:             2
##  Conditional Dist:          norm
##  h.start:                   3
##  llh.start:                 1
##  Length of Series:          4063
##  Recursion Init:            mci
##  Series Scale:              0.02703795
## 
## Parameter Initialization:
##  Initial Parameters:          $params
##  Limits of Transformations:   $U, $V
##  Which Parameters are Fixed?  $includes
##  Parameter Matrix:
##                      U           V      params includes
##     mu     -0.18874661   0.1887466  0.01904071     TRUE
##     ar1    -0.99999999   1.0000000  0.80929497     TRUE
##     ma1    -0.99999999   1.0000000 -0.83740229     TRUE
##     omega   0.00000100 100.0000000  0.10000000     TRUE
##     alpha1  0.00000001   1.0000000  0.05000000     TRUE
##     alpha2  0.00000001   1.0000000  0.05000000     TRUE
##     gamma1 -0.99999999   1.0000000  0.10000000    FALSE
##     gamma2 -0.99999999   1.0000000  0.10000000    FALSE
##     beta1   0.00000001   1.0000000  0.80000000     TRUE
##     delta   0.00000000   2.0000000  2.00000000    FALSE
##     skew    0.10000000  10.0000000  1.00000000    FALSE
##     shape   1.00000000  10.0000000  4.00000000    FALSE
##  Index List of Parameters to be Optimized:
##     mu    ar1    ma1  omega alpha1 alpha2  beta1 
##      1      2      3      4      5      6      9 
##  Persistence:                  0.9 
## 
## 
## --- START OF TRACE ---
## Selected Algorithm: nlminb 
## 
## R coded nlminb Solver: 
## 
##   0:     5457.7021: 0.0190407 0.809295 -0.837402 0.100000 0.0500000 0.0500000 0.800000
##   1:     5448.6455: 0.0190333 0.809199 -0.834878 0.0898797 0.0507276 0.0487420 0.794443
##   2:     5442.4595: 0.0190236 0.808766 -0.831926 0.0880050 0.0597887 0.0549643 0.797348
##   3:     5436.5735: 0.0189974 0.806754 -0.824995 0.0676468 0.0673191 0.0555951 0.790851
##   4:     5426.8513: 0.0189407 0.798334 -0.814997 0.0652965 0.0841722 0.0589047 0.800200
##   5:     5420.4644: 0.0188657 0.784193 -0.805863 0.0579554 0.0894687 0.0462582 0.805367
##   6:     5416.9488: 0.0187997 0.778746 -0.791786 0.0567519 0.0924213 0.0337040 0.818015
##   7:     5411.1657: 0.0186981 0.754159 -0.790889 0.0405494 0.0982159 0.0129089 0.848153
##   8:     5409.6293: 0.0186719 0.759843 -0.777127 0.0404720 0.101467 0.00912333 0.853256
##   9:     5409.5664: 0.0186700 0.759460 -0.776985 0.0374766 0.0999155 0.00701396 0.851326
##  10:     5408.4942: 0.0186691 0.759285 -0.776914 0.0388619 0.100879 0.00773575 0.852562
##  11:     5407.4262: 0.0186218 0.751330 -0.772654 0.0326713 0.103274 1.00000e-08 0.861096
##  12:     5406.9004: 0.0185367 0.750639 -0.759479 0.0221562 0.0955143 1.00000e-08 0.887414
##  13:     5405.3621: 0.0183701 0.730910 -0.742211 0.0287930 0.0798802 1.00000e-08 0.889404
##  14:     5404.8361: 0.0183677 0.729857 -0.742672 0.0262364 0.0815154 1.00000e-08 0.889227
##  15:     5404.3376: 0.0183585 0.728159 -0.743030 0.0275763 0.0838154 1.00000e-08 0.888734
##  16:     5403.9274: 0.0183443 0.726283 -0.742894 0.0272582 0.0849910 1.00000e-08 0.886500
##  17:     5403.5756: 0.0183045 0.722359 -0.741023 0.0283237 0.0882731 1.00000e-08 0.883843
##  18:     5403.0839: 0.0182023 0.716253 -0.732228 0.0286535 0.0908636 1.00000e-08 0.879550
##  19:     5402.2631: 0.0179607 0.699365 -0.723518 0.0244125 0.0840242 1.00000e-08 0.891236
##  20:     5402.2469: 0.0179604 0.699353 -0.723432 0.0245137 0.0842343 1.00000e-08 0.891350
##  21:     5402.2338: 0.0179598 0.699333 -0.723308 0.0243106 0.0843181 1.00000e-08 0.891248
##  22:     5402.2118: 0.0179556 0.699125 -0.722936 0.0243911 0.0845517 1.00000e-08 0.891348
##  23:     5401.0713: 0.0173478 0.667337 -0.681638 0.0245180 0.0839128 1.00000e-08 0.891089
##  24:     5401.0639: 0.0168868 0.635310 -0.661188 0.0386075 0.103786 1.00000e-08 0.857628
##  25:     5401.0000: 0.0168865 0.635342 -0.661084 0.0377197 0.103691 1.00000e-08 0.857496
##  26:     5400.9324: 0.0168928 0.635295 -0.660886 0.0377216 0.104160 1.00000e-08 0.858170
##  27:     5400.8528: 0.0169168 0.635010 -0.660382 0.0366528 0.104158 1.00000e-08 0.858633
##  28:     5400.7481: 0.0169731 0.634169 -0.659375 0.0362502 0.104002 1.00000e-08 0.860192
##  29:     5400.1747: 0.0179237 0.617377 -0.642442 0.0295881 0.0896161 1.00000e-08 0.880114
##  30:     5400.0218: 0.0179224 0.617490 -0.642002 0.0277450 0.0913318 1.00000e-08 0.880619
##  31:     5399.9862: 0.0179588 0.616322 -0.640785 0.0279554 0.0914910 1.00000e-08 0.881031
##  32:     5399.6615: 0.0191170 0.575338 -0.599814 0.0262848 0.0898151 1.00000e-08 0.884505
##  33:     5399.3155: 0.0191219 0.501956 -0.523692 0.0296181 0.0948942 1.00000e-08 0.875759
##  34:     5399.1778: 0.0223768 0.444831 -0.465234 0.0284471 0.0932548 1.00000e-08 0.878672
##  35:     5399.1115: 0.0232857 0.380784 -0.396861 0.0244319 0.0872102 1.00000e-08 0.889054
##  36:     5399.0129: 0.0268406 0.316476 -0.331474 0.0261076 0.0898021 1.00000e-08 0.884730
##  37:     5398.9539: 0.0308399 0.223219 -0.234907 0.0266919 0.0908727 1.00000e-08 0.883051
##  38:     5398.8284: 0.0423643 -0.0574740 0.0561819 0.0270880 0.0917394 1.00000e-08 0.881813
##  39:     5398.8228: 0.0438001 -0.0955279 0.0952419 0.0268938 0.0914146 1.00000e-08 0.882334
##  40:     5398.8150: 0.0430796 -0.0902748 0.0886937 0.0262144 0.0901917 1.00000e-08 0.884228
##  41:     5398.8139: 0.0429202 -0.0916798 0.0902033 0.0262305 0.0902800 1.00000e-08 0.884140
##  42:     5398.8123: 0.0421547 -0.0913749 0.0900517 0.0263205 0.0904446 1.00000e-08 0.883888
##  43:     5398.8123: 0.0421367 -0.0915237 0.0901895 0.0263244 0.0904327 1.00000e-08 0.883891
##  44:     5398.8123: 0.0421368 -0.0915425 0.0902024 0.0263260 0.0904336 1.00000e-08 0.883888
## 
## Final Estimate of the Negative LLH:
##  LLH:  -9270.706    norm LLH:  -2.281739 
##            mu           ar1           ma1         omega        alpha1 
##  1.139292e-03 -9.154249e-02  9.020237e-02  1.924567e-05  9.043359e-02 
##        alpha2         beta1 
##  1.000000e-08  8.838878e-01 
## 
## R-optimhess Difference Approximated Hessian Matrix:
##                   mu           ar1          ma1         omega
## mu      -6676604.439   -5272.29968    1637.1636 -6.540905e+07
## ar1        -5272.300   -3621.26368   -3538.6041 -6.970961e+05
## ma1         1637.164   -3538.60409   -3470.5155 -6.281187e+05
## omega  -65409048.823 -697096.10169 -628118.6838 -6.133251e+11
## alpha1     -3141.074     139.63518     143.5760 -2.265238e+08
## alpha2     -3999.005     177.92623     182.5247 -2.271179e+08
## beta1     -19422.674      -7.74186      13.3349 -3.055991e+08
##               alpha1        alpha2         beta1
## mu     -3.141074e+03 -3.999005e+03 -1.942267e+04
## ar1     1.396352e+02  1.779262e+02 -7.741860e+00
## ma1     1.435760e+02  1.825247e+02  1.333490e+01
## omega  -2.265238e+08 -2.271179e+08 -3.055991e+08
## alpha1 -1.236337e+05 -1.219342e+05 -1.385106e+05
## alpha2 -1.219342e+05 -1.236885e+05 -1.397871e+05
## beta1  -1.385106e+05 -1.397871e+05 -1.715156e+05
## attr(,"time")
## Time difference of 0.1562271 secs
## 
## --- END OF TRACE ---
## 
## 
## Time to Estimate Parameters:
##  Time difference of 0.733258 secs
## 
## Title:
##  GARCH Modelling 
## 
## Call:
##  garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name, 
##     include.mean = TRUE) 
## 
## Mean and Variance Equation:
##  data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1bbc0f5b8>
##  [data = d.series.name]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##          mu          ar1          ma1        omega       alpha1  
##  1.1393e-03  -9.1542e-02   9.0202e-02   1.9246e-05   9.0434e-02  
##      alpha2        beta1  
##  1.0000e-08   8.8389e-01  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##          Estimate  Std. Error  t value Pr(>|t|)    
## mu      1.139e-03   5.747e-04    1.982   0.0474 *  
## ar1    -9.154e-02   4.078e-01   -0.224   0.8224    
## ma1     9.020e-02   4.163e-01    0.217   0.8285    
## omega   1.925e-05   7.174e-06    2.683   0.0073 ** 
## alpha1  9.043e-02   1.717e-02    5.266 1.39e-07 ***
## alpha2  1.000e-08   2.491e-02    0.000   1.0000    
## beta1   8.839e-01   2.731e-02   32.360  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log Likelihood:
##  9270.706    normalized:  2.281739 
## 
## Description:
##  Thu Jan  7 16:12:34 2016 by user:  
## 
## 
## Standardised Residuals Tests:
##                                 Statistic p-Value   
##  Jarque-Bera Test   R    Chi^2  453.9605  0         
##  Shapiro-Wilk Test  R    W      0.9879195 0         
##  Ljung-Box Test     R    Q(10)  6.359994  0.7841659 
##  Ljung-Box Test     R    Q(15)  9.014066  0.8767808 
##  Ljung-Box Test     R    Q(20)  11.17128  0.9416592 
##  Ljung-Box Test     R^2  Q(10)  22.02592  0.01497309
##  Ljung-Box Test     R^2  Q(15)  27.53434  0.02467251
##  Ljung-Box Test     R^2  Q(20)  33.57461  0.02915051
##  LM Arch Test       R    TR^2   21.8295   0.03947568
## 
## Information Criterion Statistics:
##       AIC       BIC       SIC      HQIC 
## -4.560032 -4.549162 -4.560038 -4.556182

# KROT3.SA
stock.name <- "KROT3.SA"
stock.description <- "Kroton Educacional S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)
## time series starts 2012-03-14
## 'zoo' series from 2012-03-14 to 2016-01-06
##   Data: num [1:994, 1] 2.21 2.21 2.21 2.21 2.21 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "AdjClose"
##   Index:  Date[1:994], format: "2012-03-14" "2012-03-15" "2012-03-16" "2012-03-19" ...

## 'zoo' series from 2012-03-14 to 2015-09-30
##   Data: num [1:924] 2.21 2.21 2.21 2.21 2.21 ...
##   Index:  Date[1:924], format: "2012-03-14" "2012-03-15" "2012-03-16" "2012-03-19" ...

## Warning in adf.test(d.series.name): p-value smaller than printed p-value

## Warning in lsfit(log10(M), log10(RS), wt): 29 missing values deleted

## 
## Title:
##  ARIMA Modelling 
## 
## Call:
##  armaFit(formula = ~arma(1, 3), data = d.series.name)
## 
## Model:
##  ARIMA(1,0,3) with method: CSS-ML
## 
## Coefficient(s):
##       ar1        ma1        ma2        ma3  intercept  
##  0.426797  -0.560552   0.053052  -0.238926   0.001384  
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.391973 -0.011893 -0.001244  0.015092  1.275535 
## 
## Moments: 
## Skewness Kurtosis 
##   -1.295  120.049 
## 
## Coefficient(s):
##            Estimate  Std. Error  t value Pr(>|t|)    
## ar1        0.426797    0.076118    5.607 2.06e-08 ***
## ma1       -0.560552    0.074747   -7.499 6.42e-14 ***
## ma2        0.053052    0.043406    1.222    0.222    
## ma3       -0.238926    0.031674   -7.543 4.57e-14 ***
## intercept  0.001384    0.001440    0.961    0.336    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## sigma^2 estimated as: 0.00969
## log likelihood:       829.97
## AIC Criterion:        -1647.94

## 
## Description:
##  Thu Jan  7 16:12:36 2016 by user:

## Warning in lsfit(log10(M), log10(RS), wt): 29 missing values deleted

## 
## Series Initialization:
##  ARMA Model:                arma
##  Formula Mean:              ~ arma(1, 1)
##  GARCH Model:               garch
##  Formula Variance:          ~ garch(2, 1)
##  ARMA Order:                1 1
##  Max ARMA Order:            1
##  GARCH Order:               2 1
##  Max GARCH Order:           2
##  Maximum Order:             2
##  Conditional Dist:          norm
##  h.start:                   3
##  llh.start:                 1
##  Length of Series:          923
##  Recursion Init:            mci
##  Series Scale:              0.1033657
## 
## Parameter Initialization:
##  Initial Parameters:          $params
##  Limits of Transformations:   $U, $V
##  Which Parameters are Fixed?  $includes
##  Parameter Matrix:
##                      U           V      params includes
##     mu     -0.13042069   0.1304207  0.01305813     TRUE
##     ar1    -0.99999999   1.0000000 -0.52596396     TRUE
##     ma1    -0.99999999   1.0000000  0.45626181     TRUE
##     omega   0.00000100 100.0000000  0.10000000     TRUE
##     alpha1  0.00000001   1.0000000  0.05000000     TRUE
##     alpha2  0.00000001   1.0000000  0.05000000     TRUE
##     gamma1 -0.99999999   1.0000000  0.10000000    FALSE
##     gamma2 -0.99999999   1.0000000  0.10000000    FALSE
##     beta1   0.00000001   1.0000000  0.80000000     TRUE
##     delta   0.00000000   2.0000000  2.00000000    FALSE
##     skew    0.10000000  10.0000000  1.00000000    FALSE
##     shape   1.00000000  10.0000000  4.00000000    FALSE
##  Index List of Parameters to be Optimized:
##     mu    ar1    ma1  omega alpha1 alpha2  beta1 
##      1      2      3      4      5      6      9 
##  Persistence:                  0.9 
## 
## 
## --- START OF TRACE ---
## Selected Algorithm: nlminb 
## 
## R coded nlminb Solver: 
## 
##   0:     967.58942: 0.0130581 -0.525964 0.456262 0.100000 0.0500000 0.0500000 0.800000
##   1:     946.80898: 0.0130581 -0.526246 0.455994 0.0849877 0.0504835 0.0491423 0.790264
##   2:     941.35280: 0.0130579 -0.526773 0.455496 0.0699198 0.0525607 0.0485962 0.780825
##   3:     938.20876: 0.0130572 -0.528770 0.453608 0.0805589 0.0637244 0.0496474 0.772176
##   4:     936.01889: 0.0130559 -0.531357 0.451178 0.0787447 0.0735573 0.0495962 0.757730
##   5:     933.89311: 0.0130500 -0.539192 0.443934 0.0959114 0.0833502 0.0517521 0.729877
##   6:     932.39394: 0.0130443 -0.545643 0.438012 0.0908191 0.107386 0.0757073 0.724335
##   7:     932.25930: 0.0130123 -0.553081 0.431147 0.0989278 0.0933489 0.0750350 0.694113
##   8:     931.78839: 0.0130120 -0.553271 0.430965 0.103134 0.0953226 0.0765080 0.696866
##   9:     931.60029: 0.0130114 -0.553655 0.430599 0.0991742 0.0985884 0.0786114 0.697459
##  10:     931.41811: 0.0129993 -0.556044 0.428190 0.101352 0.104982 0.0720578 0.702428
##  11:     931.25579: 0.0129763 -0.557703 0.426417 0.0985900 0.112384 0.0646962 0.702315
##  12:     931.17804: 0.0128827 -0.548232 0.435006 0.103903 0.124977 0.0654636 0.692311
##  13:     931.01319: 0.0126245 -0.573829 0.409419 0.0999748 0.136144 0.0549268 0.699869
##  14:     931.00259: 0.0126239 -0.573381 0.409825 0.0993139 0.136706 0.0553676 0.699628
##  15:     930.99164: 0.0126203 -0.572839 0.410271 0.0999484 0.137192 0.0554033 0.700031
##  16:     930.97702: 0.0126075 -0.571589 0.411215 0.0991066 0.138019 0.0547034 0.700456
##  17:     930.96119: 0.0125712 -0.569293 0.412759 0.0993224 0.139346 0.0531641 0.702003
##  18:     930.93498: 0.0124562 -0.567325 0.413003 0.0989396 0.138627 0.0551729 0.700851
##  19:     930.90891: 0.0122255 -0.566167 0.411178 0.100877 0.137685 0.0590722 0.697159
##  20:     930.87405: 0.0120102 -0.562354 0.412211 0.0997537 0.142229 0.0528290 0.698606
##  21:     930.85152: 0.0117723 -0.559090 0.414083 0.100088 0.143340 0.0528754 0.700270
##  22:     930.83165: 0.0115337 -0.557912 0.414836 0.0990335 0.141898 0.0561553 0.699591
##  23:     930.75889: 0.00971934 -0.551668 0.409794 0.0988277 0.151849 0.0433092 0.699115
##  24:     930.27939: -0.00114068 -0.516561 0.379595 0.103142 0.163531 0.0522702 0.688221
##  25:     930.01328: -0.0119426 -0.435956 0.322737 0.100179 0.166044 0.0446284 0.698160
##  26:     929.73136: -0.0226798 -0.354896 0.216785 0.101193 0.156178 0.0578991 0.694307
##  27:     929.60081: -0.0299643 -0.410601 0.275530 0.102152 0.132696 0.0777366 0.690777
##  28:     929.55580: -0.0329053 -0.477743 0.335559 0.101214 0.132565 0.0781253 0.692050
##  29:     929.55554: -0.0348876 -0.436081 0.284208 0.100764 0.130674 0.0805701 0.692226
##  30:     929.55057: -0.0341590 -0.465515 0.317678 0.100888 0.131164 0.0797313 0.692133
##  31:     929.55056: -0.0341556 -0.464813 0.317285 0.100891 0.131355 0.0795513 0.692152
##  32:     929.55055: -0.0341711 -0.465080 0.317505 0.100891 0.131290 0.0795890 0.692155
##  33:     929.55055: -0.0341724 -0.465094 0.317513 0.100890 0.131296 0.0795832 0.692155
## 
## Final Estimate of the Negative LLH:
##  LLH:  -1165.182    norm LLH:  -1.262385 
##           mu          ar1          ma1        omega       alpha1 
## -0.003532254 -0.465093595  0.317512574  0.001077959  0.131295992 
##       alpha2        beta1 
##  0.079583204  0.692155043 
## 
## R-optimhess Difference Approximated Hessian Matrix:
##                   mu        ar1          ma1         omega       alpha1
## mu     -128480.59912  197.32587   -99.984334  6.906563e+05   -575.83877
## ar1        197.32587 -217.76756  -201.662115  6.182968e+03     55.48211
## ma1        -99.98433 -201.66211  -194.416743  1.006964e+04     42.66468
## omega   690656.27134 6182.96839 10069.639030 -3.158162e+08 -97893.80662
## alpha1    -575.83877   55.48211    42.664676 -9.789381e+04  -1099.55414
## alpha2   -2774.72114   14.70127    -7.695865 -8.393257e+04  -1090.21732
## beta1     -228.62597   88.37801    88.268715 -1.154244e+06  -1584.54527
##               alpha2         beta1
## mu      -2774.721135 -2.286260e+02
## ar1        14.701266  8.837801e+01
## ma1        -7.695865  8.826871e+01
## omega  -83932.570964 -1.154244e+06
## alpha1  -1090.217315 -1.584545e+03
## alpha2  -1560.334134 -2.090775e+03
## beta1   -2090.775041 -7.710301e+03
## attr(,"time")
## Time difference of 0.05019403 secs
## 
## --- END OF TRACE ---
## 
## 
## Time to Estimate Parameters:
##  Time difference of 0.14305 secs
## 
## Title:
##  GARCH Modelling 
## 
## Call:
##  garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name, 
##     include.mean = TRUE) 
## 
## Mean and Variance Equation:
##  data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b57e64e0>
##  [data = d.series.name]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##         mu         ar1         ma1       omega      alpha1      alpha2  
## -0.0035323  -0.4650936   0.3175126   0.0010780   0.1312960   0.0795832  
##      beta1  
##  0.6921550  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##          Estimate  Std. Error  t value Pr(>|t|)    
## mu     -0.0035323   0.0030173   -1.171   0.2417    
## ar1    -0.4650936   0.3648070   -1.275   0.2023    
## ma1     0.3175126   0.3879403    0.818   0.4131    
## omega   0.0010780   0.0001064   10.134   <2e-16 ***
## alpha1  0.1312960   0.0569969    2.304   0.0212 *  
## alpha2  0.0795832   0.0594417    1.339   0.1806    
## beta1   0.6921550   0.0270258   25.611   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log Likelihood:
##  1165.182    normalized:  1.262385 
## 
## Description:
##  Thu Jan  7 16:12:37 2016 by user:  
## 
## 
## Standardised Residuals Tests:
##                                 Statistic p-Value     
##  Jarque-Bera Test   R    Chi^2  3935116   0           
##  Shapiro-Wilk Test  R    W      0.3097579 0           
##  Ljung-Box Test     R    Q(10)  27.76416  0.001968995 
##  Ljung-Box Test     R    Q(15)  39.54696  0.0005306483
##  Ljung-Box Test     R    Q(20)  40.11346  0.004832976 
##  Ljung-Box Test     R^2  Q(10)  5.702808  0.8395835   
##  Ljung-Box Test     R^2  Q(15)  6.09349   0.9781342   
##  Ljung-Box Test     R^2  Q(20)  6.132036  0.9987071   
##  LM Arch Test       R    TR^2   5.873323  0.9223325   
## 
## Information Criterion Statistics:
##       AIC       BIC       SIC      HQIC 
## -2.509603 -2.472990 -2.509717 -2.495634

# VALE5.SA
stock.name <- "VALE5.SA"
stock.description <- "Vale S.A."
# Call your function and pass x and y to the function
run <- generateAnalysis(stock.name,stock.description)
## time series starts 2003-01-01
## 'zoo' series from 2003-01-01 to 2016-01-06
##   Data: num [1:3228, 1] 6.07 6.07 6 5.84 5.71 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "AdjClose"
##   Index:  Date[1:3228], format: "2003-01-01" "2003-01-02" "2003-01-03" "2003-01-06" ...

## 'zoo' series from 2003-01-01 to 2015-09-30
##   Data: num [1:3158] 6.07 6.07 6 5.84 5.71 ...
##   Index:  Date[1:3158], format: "2003-01-01" "2003-01-02" "2003-01-03" "2003-01-06" ...

## Warning in adf.test(d.series.name): p-value smaller than printed p-value

## 
## Title:
##  ARIMA Modelling 
## 
## Call:
##  armaFit(formula = ~arma(1, 3), data = d.series.name)
## 
## Model:
##  ARIMA(1,0,3) with method: CSS-ML
## 
## Coefficient(s):
##        ar1         ma1         ma2         ma3   intercept  
## -0.1147017   0.1352835  -0.0466870  -0.0628895   0.0002432  
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.1591899 -0.0125681  0.0002449  0.0123261  0.1234791 
## 
## Moments: 
## Skewness Kurtosis 
##  -0.0741   3.2827 
## 
## Coefficient(s):
##             Estimate  Std. Error  t value Pr(>|t|)   
## ar1       -0.1147017   0.2806508   -0.409  0.68276   
## ma1        0.1352835   0.2799768    0.483  0.62896   
## ma2       -0.0466870   0.0185914   -2.511  0.01203 * 
## ma3       -0.0628895   0.0207959   -3.024  0.00249 **
## intercept  0.0002432   0.0003799    0.640  0.52203   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## sigma^2 estimated as: 0.0005368
## log likelihood:       7406.32
## AIC Criterion:        -14800.64

## 
## Description:
##  Thu Jan  7 16:12:40 2016 by user:

## 
## Series Initialization:
##  ARMA Model:                arma
##  Formula Mean:              ~ arma(1, 1)
##  GARCH Model:               garch
##  Formula Variance:          ~ garch(2, 1)
##  ARMA Order:                1 1
##  Max ARMA Order:            1
##  GARCH Order:               2 1
##  Max GARCH Order:           2
##  Maximum Order:             2
##  Conditional Dist:          norm
##  h.start:                   3
##  llh.start:                 1
##  Length of Series:          3157
##  Recursion Init:            mci
##  Series Scale:              0.02324454
## 
## Parameter Initialization:
##  Initial Parameters:          $params
##  Limits of Transformations:   $U, $V
##  Which Parameters are Fixed?  $includes
##  Parameter Matrix:
##                      U           V      params includes
##     mu     -0.10373679   0.1037368  0.01037722     TRUE
##     ar1    -0.99999999   1.0000000 -0.29796748     TRUE
##     ma1    -0.99999999   1.0000000  0.32712119     TRUE
##     omega   0.00000100 100.0000000  0.10000000     TRUE
##     alpha1  0.00000001   1.0000000  0.05000000     TRUE
##     alpha2  0.00000001   1.0000000  0.05000000     TRUE
##     gamma1 -0.99999999   1.0000000  0.10000000    FALSE
##     gamma2 -0.99999999   1.0000000  0.10000000    FALSE
##     beta1   0.00000001   1.0000000  0.80000000     TRUE
##     delta   0.00000000   2.0000000  2.00000000    FALSE
##     skew    0.10000000  10.0000000  1.00000000    FALSE
##     shape   1.00000000  10.0000000  4.00000000    FALSE
##  Index List of Parameters to be Optimized:
##     mu    ar1    ma1  omega alpha1 alpha2  beta1 
##      1      2      3      4      5      6      9 
##  Persistence:                  0.9 
## 
## 
## --- START OF TRACE ---
## Selected Algorithm: nlminb 
## 
## R coded nlminb Solver: 
## 
##   0:     4220.5083: 0.0103772 -0.297967 0.327121 0.100000 0.0500000 0.0500000 0.800000
##   1:     4216.4468: 0.0103774 -0.296902 0.328160 0.0816230 0.0481218 0.0498433 0.791563
##   2:     4202.4737: 0.0103776 -0.295404 0.329616 0.0777685 0.0600405 0.0645020 0.797769
##   3:     4198.9154: 0.0103780 -0.292750 0.332172 0.0587052 0.0616100 0.0704353 0.797734
##   4:     4194.2747: 0.0103790 -0.287891 0.336765 0.0546845 0.0600077 0.0768558 0.815341
##   5:     4190.1470: 0.0103804 -0.284722 0.339464 0.0456379 0.0492084 0.0747525 0.829284
##   6:     4182.8614: 0.0103854 -0.293368 0.328157 0.0237297 0.0227754 0.0634317 0.889690
##   7:     4182.8353: 0.0103855 -0.293172 0.328344 0.0242027 0.0229698 0.0634197 0.890115
##   8:     4182.7486: 0.0103855 -0.292912 0.328582 0.0238916 0.0227839 0.0629200 0.890215
##   9:     4182.6518: 0.0103857 -0.292277 0.329168 0.0241073 0.0229477 0.0622721 0.891122
##  10:     4182.4173: 0.0103860 -0.291210 0.330102 0.0232492 0.0231238 0.0604766 0.892623
##  11:     4181.8799: 0.0103880 -0.288251 0.332266 0.0205962 0.0275671 0.0531453 0.899710
##  12:     4181.7725: 0.0103902 -0.287643 0.331915 0.0206318 0.0271576 0.0478972 0.902241
##  13:     4181.6885: 0.0103916 -0.287509 0.331421 0.0214289 0.0281363 0.0463689 0.904001
##  14:     4181.5292: 0.0103931 -0.288049 0.330189 0.0206087 0.0297673 0.0449076 0.903903
##  15:     4181.5001: 0.0103932 -0.287721 0.330471 0.0201571 0.0303208 0.0450884 0.904273
##  16:     4181.4903: 0.0103942 -0.287342 0.330390 0.0197856 0.0303187 0.0443849 0.904545
##  17:     4181.4478: 0.0103953 -0.287039 0.330247 0.0198494 0.0306317 0.0438646 0.905156
##  18:     4181.3822: 0.0104005 -0.285592 0.329373 0.0192441 0.0316866 0.0409189 0.907264
##  19:     4181.3710: 0.0104263 -0.279882 0.323830 0.0193311 0.0323208 0.0402627 0.908013
##  20:     4181.3098: 0.0104526 -0.273730 0.318727 0.0190792 0.0318363 0.0407459 0.907759
##  21:     4181.2973: 0.0104687 -0.271159 0.314781 0.0187759 0.0339347 0.0392624 0.907976
##  22:     4181.2557: 0.0105059 -0.262338 0.309281 0.0185062 0.0324165 0.0406556 0.907948
##  23:     4181.1332: 0.0107154 -0.225419 0.269950 0.0185378 0.0351948 0.0352990 0.909883
##  24:     4181.1144: 0.0107154 -0.225398 0.269969 0.0186356 0.0353079 0.0354033 0.909986
##  25:     4181.1067: 0.0107155 -0.225321 0.270037 0.0184745 0.0353859 0.0354492 0.909975
##  26:     4181.1030: 0.0107170 -0.225004 0.269834 0.0184924 0.0354696 0.0355134 0.910044
##  27:     4181.0977: 0.0107201 -0.224394 0.269340 0.0184091 0.0354496 0.0354811 0.910031
##  28:     4181.0908: 0.0107263 -0.223166 0.268353 0.0183983 0.0355081 0.0355120 0.910119
##  29:     4180.9833: 0.0109980 -0.172220 0.223144 0.0180002 0.0344977 0.0344766 0.912143
##  30:     4180.9145: 0.0114051 -0.128679 0.179729 0.0186784 0.0347649 0.0367378 0.909781
##  31:     4180.8614: 0.0120147 -0.0981896 0.148996 0.0186760 0.0350652 0.0374611 0.907772
##  32:     4180.6286: 0.0167261 -0.146222 0.195989 0.0160406 0.0423852 0.0262607 0.914594
##  33:     4179.9863: 0.0278852 -0.108362 0.160499 0.0179731 0.0452981 0.0268463 0.909684
##  34:     4179.8759: 0.0389712 -0.201948 0.254826 0.0190505 0.0349392 0.0366266 0.908425
##  35:     4179.7971: 0.0401254 -0.153606 0.203991 0.0186412 0.0361799 0.0364379 0.908242
##  36:     4179.7723: 0.0387613 -0.153286 0.204185 0.0186518 0.0387350 0.0342847 0.907902
##  37:     4179.7712: 0.0380231 -0.145066 0.196369 0.0185615 0.0395751 0.0330278 0.908373
##  38:     4179.7707: 0.0379510 -0.149362 0.200467 0.0185766 0.0395148 0.0333839 0.908112
##  39:     4179.7706: 0.0380834 -0.148776 0.199910 0.0185871 0.0394370 0.0334200 0.908129
##  40:     4179.7706: 0.0380611 -0.148700 0.199835 0.0185843 0.0394510 0.0334001 0.908138
##  41:     4179.7706: 0.0380622 -0.148710 0.199845 0.0185846 0.0394502 0.0334020 0.908137
## 
## Final Estimate of the Negative LLH:
##  LLH:  -7695.869    norm LLH:  -2.437716 
##            mu           ar1           ma1         omega        alpha1 
##  8.847391e-04 -1.487097e-01  1.998448e-01  1.004141e-05  3.945024e-02 
##        alpha2         beta1 
##  3.340199e-02  9.081366e-01 
## 
## R-optimhess Difference Approximated Hessian Matrix:
##                   mu           ar1           ma1         omega
## mu      -5804399.013 -3.054037e+03  1.286124e+03 -5.248985e+07
## ar1        -3054.037 -3.052770e+03 -3.071717e+03 -1.265958e+06
## ma1         1286.124 -3.071717e+03 -3.117684e+03 -1.186777e+06
## omega  -52489849.142 -1.265958e+06 -1.186777e+06 -1.454973e+12
## alpha1      1319.787  6.021266e+01  5.899689e+01 -3.943726e+08
## alpha2     -7751.153 -3.789274e+01 -3.491994e+01 -3.932371e+08
## beta1     -28331.208 -5.595683e+02 -5.343574e+02 -5.055202e+08
##               alpha1        alpha2         beta1
## mu      1.319787e+03 -7.751153e+03 -2.833121e+04
## ar1     6.021266e+01 -3.789274e+01 -5.595683e+02
## ma1     5.899689e+01 -3.491994e+01 -5.343574e+02
## omega  -3.943726e+08 -3.932371e+08 -5.055202e+08
## alpha1 -1.605027e+05 -1.591281e+05 -1.736106e+05
## alpha2 -1.591281e+05 -1.612429e+05 -1.754598e+05
## beta1  -1.736106e+05 -1.754598e+05 -2.079402e+05
## attr(,"time")
## Time difference of 0.1205029 secs
## 
## --- END OF TRACE ---
## 
## 
## Time to Estimate Parameters:
##  Time difference of 0.4151878 secs
## 
## Title:
##  GARCH Modelling 
## 
## Call:
##  garchFit(formula = ~arma(1, 1) + garch(2, 1), data = d.series.name, 
##     include.mean = TRUE) 
## 
## Mean and Variance Equation:
##  data ~ arma(1, 1) + garch(2, 1)
## <environment: 0x7fd1b9ab7d78>
##  [data = d.series.name]
## 
## Conditional Distribution:
##  norm 
## 
## Coefficient(s):
##          mu          ar1          ma1        omega       alpha1  
##  8.8474e-04  -1.4871e-01   1.9984e-01   1.0041e-05   3.9450e-02  
##      alpha2        beta1  
##  3.3402e-02   9.0814e-01  
## 
## Std. Errors:
##  based on Hessian 
## 
## Error Analysis:
##          Estimate  Std. Error  t value Pr(>|t|)    
## mu      8.847e-04   4.451e-04    1.988 0.046835 *  
## ar1    -1.487e-01   2.080e-01   -0.715 0.474662    
## ma1     1.998e-01   2.058e-01    0.971 0.331439    
## omega   1.004e-05   2.712e-06    3.702 0.000214 ***
## alpha1  3.945e-02   1.738e-02    2.270 0.023202 *  
## alpha2  3.340e-02   2.103e-02    1.588 0.112285    
## beta1   9.081e-01   1.456e-02   62.383  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Log Likelihood:
##  7695.869    normalized:  2.437716 
## 
## Description:
##  Thu Jan  7 16:12:41 2016 by user:  
## 
## 
## Standardised Residuals Tests:
##                                 Statistic p-Value     
##  Jarque-Bera Test   R    Chi^2  158.6731  0           
##  Shapiro-Wilk Test  R    W      0.9921676 4.212096e-12
##  Ljung-Box Test     R    Q(10)  12.27084  0.2673392   
##  Ljung-Box Test     R    Q(15)  24.79349  0.05278648  
##  Ljung-Box Test     R    Q(20)  27.02037  0.1346918   
##  Ljung-Box Test     R^2  Q(10)  11.04974  0.3536558   
##  Ljung-Box Test     R^2  Q(15)  14.87996  0.4600981   
##  Ljung-Box Test     R^2  Q(20)  16.74909  0.6692009   
##  LM Arch Test       R    TR^2   12.86545  0.3788956   
## 
## Information Criterion Statistics:
##       AIC       BIC       SIC      HQIC 
## -4.870997 -4.857566 -4.871007 -4.866178